1. Ion Beam Analysis (IBA)
IBA uses incident ions to probe the sample
SIMS
RBS
Gives composition vs. depth
ERD
NRA
IIX
Channeling

2. IBA 2 ways in which ions interact with matter and lose energy Elastic
Collisions
Inelastic
Collisions
Coulomb interaction
between ion and
nuclear cores
(Rutherford scattering)
Produces recoil atoms
Ion interacts with atomic electrons in solid and loses energy

3. IBA Elastic collisions :
Interaction between ion and nuclear core (Rutherford scattering)
Described as binary collision
Before collision
M0, E0 Mr
After collision
Mr, Er q f
M0, Es

4. IBA Incident ion transfers kinetic energy to recoiling particle
Conservation of energy and momentum :
Er = 4 E0 MoMrcos2q/(M0+Mr)2
Can measure energy of recoiling particle (principle of SIMS & ERD)
After collision
Mr, Er
M0, E0 q
M0, Es f

5. IBA Incident ion loses energy as it propagates through sample
Conservation of energy and momentum (for elastic collisions): 2
Es = E0 (Mr2 – M02sin2f)½ + M0cosf
M0 + Mr
Can measure energy of scattered incident ion (principle of RBS)
After collision
Mr, Er
M0, E0 q
M0, Es f

6. dE/dx = - N [ Se(E) + Sn(E) ]
IBA
Inelastic collisions :
Due to interaction of ions with electrons
Total rate of energy loss:
dE/dx = - N [ Se(E) + Sn(E) ]
stopping
power
[eV/Å]
target
atom
density
[cm-3]
nuclear
stopping
cross-section
[eV cm2]
electronic
stopping
cross-section
[eV cm2]
e.g., for 1 keV Ar+ ions in Al
dE/dx = 39 eV/Å

7. IBA RBS SIMS ERD IIX NRA dE/dx E ~ MeV’s ~ 1 keV
nuclear elastic scattering
electronic inelastic scattering E
~ MeV’s
~ 1 keV
RBS
ERD
IIX
NRA
SIMS
Detection of scattered ions (incident or recoil) and their energies gives information on sample

8. SIMS Secondary ion mass spectrometry Incident ion beam mass analyzer
1 – 20 keV
Ar+, Cs+, O+
Sputtered atoms are sorted by mass (mass analyzed)
Sputtered surface recedes
Gives composition versus depth
mass
analyzer
incident ion
(e.g., Ar+)
sputtered
atoms
sample

9. SIMS Static SIMS vs Dynamic SIMS
Compositional mapping achieved by scanning incident ion beam across the sample surface
Lateral resolution ~ 100 mm
from Feldman and Mayer, Fig. 4.7,
p. 81

10. SIMS
Applications :
Determine presence and location (depth and lateral position) of impurities or dopants (dopant profiling)
Measures the dopant profile not the carrier density
From LaPierre, Ph.D. thesis O C 2H

11. SIMS Depth calibration Measure ion current Use calibration layers
Measure etch pit depth (e.g., stylus profilometry)
Errors
At large depths (long sputtering times) bottom of crater can become rough
Sputtering of crater walls
Ion-induced mixing/implantation

12. SIMS
Depth resolution
~ 5 – 10 Å = depth from which sputtered atoms are emitted
from Stradling and Klipstein, Fig. 2, p. 89

13. SIMS Quantification Y = # sputtered (ejected) target atoms
# incident ions
[Y] = atoms/ion
Typical sputtering yields are between 0.1 and 4
From Ohring, Table 3-4, p. 113

14. SIMS Quantification
In SIMS, charged ions are detected and mass analyzed
Y+ = secondary ion yield
= # sputtered ions
# sputtered atoms
[Y+] = ions/atom

15. SIMS Quantification Y+ ~ 10-4 - 1
from Feldman and Mayer, Fig. 4.13(a), p. 86

16. SIMS Quantification A general theory to explain Y+ does not exist
Y+ depends on many factors
Surface conditions (e.g., oxidation)
Ion species being sputtered
Sputtered ion energy
Sample composition
Positive ion yield frequently enhanced when using O2- beams
Negative ion yield frequently enhanced when using Cs+ beams

17. SIMS Quantification
Comparison with known sample required for absolute quantitative analysis
But, SIMS is highly sensitive, ~ 1016 cm-3

18. RBS Rutherford Backscattering Spectrometry
Light, 1-3 MeV ions (e.g., 4He) backscatter from target atoms (Rutherford scattering)
Measure energy of backscattered ions
Gives composition versus depth
Transmitted beam
from Chu et al, Fig. 2.4, p. 28

19. RBS
from Chu et al, Fig. 6.1, p. 154
Ions detected by solid state (Si) detector, similar to EDX detector

20. RBS
From Ohring, Fig. 6-23, p. 293

21. RBS Elastic collisions :
Interaction between ion and nuclear core (Rutherford scattering)
Described as binary collision
Before collision
M0, E0 M2 Mr
After collision
M0, E0
Mr, Er q
M0, Es f

22. RBS K = kinematic factor = Es/E0 = (Mr2 – M02sin2f)½ + M0cosf 2
M0 + Mr
Incident ion: M0, E0 known
Detection angle fixed: f known
K measured for backscattered ion
Can determine Mr (atomic components of sample)
After collision
M0, E0
Mr, Er q
M0, Es f

23. RBS Eo Carbon Substrate Es1 (Au) Es2 (Si) Es3 (O) Es4 (C)
Example: impurities on a surface Eo
Carbon
Substrate
Es1 (Au)
Es2 (Si)
Es3 (O)
Es4 (C)
from Chu et al, Fig. 5.1, p. 124

24. RBS K increases with M2 → peak position identifies element
from Feldman and Mayer, Fig. 2.2,
p. 16
from Chu et al, Fig. 5.1, p. 124

25. RBS Ions scattered throughout depth of film
Ions lose energy during transit in film primarily due to inelastic electron scattering
After collision
Mr, Er
M0, E0 q
M0, Es f
M0, Es - DE

26. RBS
From Ohring, Fig. 6-21, p. 290

27. RBS
Typical RBS spectrum
From Ohring, Fig. 6-21, p. 290

28. RBS
From Ohring, Fig. 6-24, p. 295

29. RBS Energy of leading edge gives element identification
From Ohring, Fig. 6-21, p. 290

30. RBS Width of peak related to film thickness
Can convert energy scale to depth scale
From Ohring, Fig. 6-21, p. 290

31. RBS Depth Scale Ions lose energy at the rate dE/dx (stopping power)
From Ohring
From Ohring, Fig. 6-21, p. 290
Ions lose energy at the rate dE/dx (stopping power)
Incident path, x = - ∫ dE / (dE/dx)
Outgoing path, x = - ∫ dE / (dE/dx) E2 E1 E4 E3
Stopping power, dE/dx, varies with energy, E

32. RBS Depth Scale dE/dx varies with energy dE/dx E ~ keV’s ~ MeV’s
nuclear elastic scattering
electronic inelastic scattering E
~ keV’s
~ MeV’s

33. RBS Depth Scale Approximation (valid for thin films) :
(dE/dx)incident path ~ dE/dx at E1
(dE/dx)outgoing path ~ dE/dx at E4
From Ohring, Fig. 6-21, p. 290

34. RBS Depth Scale Incident path: x = - ∫ dE / (dE/dx)E1
= - (E2 – E1) / (dE/dx)E1
Outgoing path:
x = - ∫ dE / (dE/dx)E4
= - (E4 – E3) / (dE/dx)E4
= - (E4 – KE2) / (dE/dx)E4
Can eliminate E2 and solve for x E2 E1 E4 E3

35. RBS Depth Scale x = (KE1 – E4) / [ K (dE/dx)E1 + (dE/dx)E4 ]
E1 , (dE/dx)E1, (dE/dx)E4 are known
Measure E1, E4
Can determine x
Depth resolution ~ nm (determined by energy resolution of MCA ~ few keV)
From Ohring, Fig. 6-21, p. 290

36. RBS Height of peak gives amount of element present
From Ohring, Fig. 6-21, p. 290

37. RBS Quantification
The number of backscattered ions gives the composition
# scattered particles :
Y = Q (Nt) (ds/dW) W
detector solid angle
total # of incident ions
# atoms per unit area
Differential scattering cross-section = scattering cross-section per unit solid angle, W
ds/dW given by famous Rutherford scattering formula :
ds/dW ~ (Z1Z2e2 / 4Eo)2 sin-4(f/2)

38. RBS Quantification Example: impurities on a surface
Peak position identifies element
Peak height identifies amount of element Eo
Carbon
Substrate
Es1 (Au)
Es2 (Si)
Es3 (O)
Es4 (C)
from Chu et al, Fig. 5.1, p. 124

39. RBS Quantification Quantification Method 1: Theoretical
Amount of impurity per unit area =
(Nt)i = Yi / [ Q (ds/dW)i W]
If geometry (W, f) is well known
from Chu et al, Fig. 5.1, p. 124

40. RBS Quantification Quantification
Method 2: Comparison with substrate peak
Substrate:
Ys = Q {Ns [dE/(dE/dx)s]} (ds/dW)sW
depth, x, corresponding to dE
One energy channel ~ few keV Ys
from Chu et al, Fig. 5.1, p. 124

41. RBS Quantification Quantification Method 2: Comparison with substrate
Impurity Atom:
Yi = Q (Ni t) (ds/dW)s W Ys
from Chu et al, Fig. 5.1, p. 124

42. RBS Quantification Quantification Method 2: Comparison with substrate
Ratio:
Yi / Ys = (dsi/dW)i (Nt)i
(dss/dW)s Ns dE/(dE/dx)s
ds/dW ~ Z2
Yi / Ys = Zi (Nt)i
Zs2 Ns dE / (dE/dx)s
(Nt)i = (Yi/Ys) (Zs/Zi)2 [Ns dE / (dE/dx)s]

43. RBS Quantification Sensitivity ~ 1012 – 1014 cm-2 ~ 1 at %
Lateral resolution ~ mm to mm
MCA detects energy difference of a few keV → determines region of good mass resolution
from Feldman and Mayer, Fig. 2.2, p. 16

44. RBS Major advantage of RBS Quantitative capability Problem with RBS :
Difficult to detect light elements in a heavy mass substrate
Overlap produces small signal on large background
Problem solved by using ERD
adapted from Chu et al., Fig. 8.21, p. 248

45. ERD Mr, Er q After collision f M0, Es M0, E0
Elastic Recoil Detection :
Use light MeV ions at glancing incidence; e.g., 4He
Detect energy of recoiling atoms
Gives composition versus depth
Useful for light element detection in sample (e.g., H, D)
Mr, Er q
After collision f
M0, Es
M0, E0

46. ERD detector Al foil Mr, Er q After collision f M0, Es M0, E0
Elastic Recoil Detection :
Al foil blocks backscattered (incident) ions (M0, E0); ds/dW ~ Z2
Lighter recoil atoms (M2, E2) pass to detector
detector
Al foil
Mr, Er q
After collision f
M0, Es
M0, E0

47. ERD Mr, Er q After collision f M0, Es M0, E0
= Er/E0 = [ 4M0Mr / (M0 + Mr)2 ] cos2q
Incident ion: M0, E0 known
Detection angle fixed: q known
g measured for backscattered ion
Can determine Mr (atomic components of sample) versus depth
Mr, Er q
After collision f
M0, Es
M0, E0

48. IIX After collision M0, E0 Mr M0, Es Ion Beam Induced X-ray Emission :
Light MeV ion causes inner shell ionization
Outer shell electron fills vacancy
Measure energy of characteristic x-ray emission → Identify atomic species
Similar to EDX
After collision
M0, E0 Mr
M0, Es

49. IIX
Typical IIX Spectrum
from Mayer and Rimini, Fig. 5.1, p. 315

50. IIX Quantification
Can determine amount of element present by measuring x-ray line intensity (same as EDX)
Solid state (Si) detector
Intensity of x-rays from a depth d is :
I = Q(d)cswx e-md/cosq e dW/4p
Q(d) = intensity of ion-beam at depth d
c = atomic concentration
s = ionization cross-section
wx = x-ray yield (fluorescence yield)
m = x-ray absorption coefficient
e = detector efficiency
dW = detector solid angle
q = detector angle wrt ion-beam

51. energy released due to mass difference
NRA
Nuclear Reaction Analysis :
Light MeV ions produce nuclear reaction with atomic species in target
Detect reaction products
X + a → Y + b + Q
e.g., 12C + d → 13C + p MeV
denoted as 12C(d, p)13C
energy released due to mass difference
target
atom
incident
ion
resulting
atom
reactant
product

52. Before collision After collision
NRA
Use geometry similar to RBS
Measure energy of particle b
Before
collision
Ma, Ea a Mx X
After
collision
Mb, Eb b
Ma, Ea a q
My, Ey Y f

53. NRA Eb = [ A ± (A2 + B)½ ]2 A = (MaMbEa)½cosq Mb + My
B = MyQ + Ea (My – Ma)
Q = (Mx+Ma)c2 – (My+Mb)c2
After
collision
Mb, Eb b
Ma, Ea a q
My, Ey Y f

54. Eb is characteristic of the reaction
NRA
Eb is characteristic of the reaction
Can determine Mx (species in target sample)
Use thin foil to block backscattered ions (Ma, Ea)
detector
Al foil
After
collision
Mb, Eb b
Ma, Ea a q
My, Ey Y f

55. NRA
Sensitivity ~ 10-3 at %
from Mayer and Rimini, Table 4.2, p. 118

56. Channeling
Ions incident along a major crystallographic orientation experience channeling effect
RBS backscattering yield is reduced

57. Can detect light elements in larger mass matrix
Channeling
Can detect light elements in larger mass matrix
from Chu et al., Fig. 8.21, p. 248

58. e.g., amorphous Si on crystalline Si
Channeling
e.g., amorphous Si on crystalline Si
from Mayer and Rimini, Fig. 3.3, p. 78

59. Summary
From Ohring, Table 6-3, p. 276